Former national security adviser Michael Flynn has offered to cooperate with congressional investigators in exchange for immunity from prosecution, a suggestion that has been met with initial skepticism, according to people familiar with the matter.

“General Flynn certainly has a story to tell, and he very much wants to tell it, should the circumstances permit,’’ Flynn’s attorney, Robert Kelner, said in a statement Thursday evening. “Out of respect for the committees, we will not comment right now on the details of discussions between counsel for General Flynn and the House and Senate intelligence committees, other than to confirm that those discussions have taken place. But it is important to acknowledge the circumstances in which those discussions are occurring.’’

The committees are both looking into whether any associates of Donald Trump may have coordinated with agents of the Russian government seeking to meddle in last year’s presidential election. The FBI is also investigating. The Trump administration has denied any such coordination.

The offer by Flynn’s lawyer was first reported by the Wall Street Journal. Flynn’s overture seemed to have been aimed principally at the Senate committee, as Democrats on the House committee said they had not received word of an offer of testimony for immunity.

(Daron Taylor,Jhaan Elker/The Washington Post)

Officials said the idea of immunity for Flynn — who is considered a central figure in the probes because of his contacts with the Russian ambassador to the United States — was a “non-starter,’’ particularly at such an early stage of the investigations. A wide-ranging grant of immunity could protect Flynn from potential future charges from the Justice Department, but Congress has the power to grant only limited “testimonial” immunity, which means prosecutors cannot use witnesses’ testimony against them in any prosecution. Ultimately, it is Justice’s decision whether to grant immunity from prosecution for any underlying conduct that is discussed, or other matters that don’t come up in testimony.

On Friday, a tweet by President Trump appeared to support Flynn’s offer, saying his former security adviser “should ask for immunity.”

It is not unheard of for potential congressional witnesses to seek immunity in exchange for testimony. During the Obama administration, former IRS official Lois Lerner sought immunity for her testimony to Congress, which was investigating how she and other officials scrutinized conservative groups. The FBI was also investigating the matter at the time. The committee declined to grant her immunity, and she was still called to testify at a hearing, in which she repeatedly invoked her Fifth Amendment right to protect herself against self-incrimination.

Flynn’s attorney said his client, a decorated former general, was now the subject of “unfounded allegations, outrageous claims of treason, and vicious innuendo.’’

The lawyer added: “No reasonable person, who has the benefit of advice from counsel, would submit to questioning in such a highly politicized, witch hunt environment without assurances against unfair prosecution.’’

Peter Zeidenberg, a former federal prosecutor and an assistant special counsel in the prosecution of I. Lewis “Scooter” Libby, said that the Senate committee apparently did not “want to screw up a possible prosecution.”

But, he added, “there may be things more important than getting a prosecution of Flynn.” Such as learning the extent of contacts between Trump associates and Russian officials. “That is a compelling and urgent need. A prosecution of Flynn could take several years. I wouldn’t want them to wait that long to find out what Flynn knows.”